Tag Archives: singapore maths

Mastery learning is the belief that students should master a skill before moving on to learn a new one. In contrast to the classic spiral curriculum, where students raced between topics without properly learning any of them, a mastery curriculum gives students the space to learn a skill, understand it conceptually, and practise until it’s automatic.

This approach matters because of its effect on working memory. Students who have mastered previous skills have their working memory freed to learn new ones, while students who haven’t get bogged down in the basics and don’t have the working memory space to learn something new.

There are some important subtleties of definition that Steve Chinn picks up on. What it means to have mastered a topic must be clearly defined from the outset, or confusion will ensue. As understanding improves when students develop their conceptual map of maths and draw links between topics, we know that mastery early in school will not mean perfection. For me, mastery means two things:

The student can demonstrate or explain the concept orally, concretely, visually and abstractly.

The student can apply the concept automatically, so that it is not dominating their working memory.

Chinn does not engage with these fundamentals of mastery learning.

His first criticism is that mastery learning will not help children catch up, and that they should instead be taught with an emphasis “on understanding maths concepts”. Given that Singapore Maths and its mastery model is renowned for its focus on developing understanding, this seems like an odd criticism. Conceptual understanding is at the heart of mastery learning, especially of Singapore Maths and its concrete-pictorial-abstract model of learning mathematical concepts.

His second criticism is that mastery learning is flawed because the ordering of skills for teaching is imperfect. This is true – there is no universally accepted hierarchy of all skills. This does not detract from the obvious fact that some skills are dependent on others, and that these dependencies are important for the order in which we teach. Adding fractions requires a knowledge of lowest common multiples, which requires a knowledge of times tables. We may disagree on whether we should teach names of shapes or bar charts first in the gap between them, but we know they have to come in that order.

The next criticism is that mastery learning is flawed because some people, for unknown reasons, appear to learn things differently. Even if we accept this argument, I cannot see where it leads. Is the implication that we therefore don’t need to care about the order in which we teach topics, and should pull them from a hat? If order doesn’t matter for some people, why deprive the others of being taught in a logical sequence?

It is particularly dangerous to support such arguments with anecdotal success stories like the dyslexic maths student whose times table recall was not perfect. Anecdotes do not a policy make. This anecdote seems compelling precisely because it is so rare, and it is so rare because it is an exception to a large body of well established research. This student succeeded in spite of imperfect times tables, not because of them. That they succeeded against the odds is not a reason for us to stack the odds against everybody else.